\newproblem{lay:4_6_26}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.6.26}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	In statistical theory, a common requirement is that a matrix be of \textit{full rank}. That is, the rank should be as large as possible.
	Explain why an $m\times n$ matrix with more rows than columns has full rank if and only if its columns are linearly independent.
}{
  % Solution
	The if there are more rows than columns then $m>n$ and the rank can be at most $n$. The rank is $n$ iff the dimension of the column space is $n$. But
	since there are only $n$ columns in the matrix, this can only be achieved if they are linearly independent.
}
\useproblem{lay:4_6_26}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
